Structural Concrete - Hassoun

192 Chapter 5 Shear and Diagonal Tension
of these forces. The location of cracks in the concrete beam depends on the direction of principal
stresses. For the combined action of normal stresses and shear stresses, maximum diagonal tension
may occur at about a distance d from the face of the support.
The behavior of reinforced concrete beams with and without shear reinforcement tested under
increasing load was discussed in Section 3.3. In the tested beams, vertical flexural cracks developed
at the section of maximum bending moment when the tensile stresses in concrete exceeded the
modulus of rupture of concrete, or f r = 7.5λ √ f ′ c. Inclined cracks in the web developed at a later
stage at a location very close to the support.
An inclined crack occurring in a beam that was previously uncracked is generally referred to as
a web-shear crack. If the inclined crack starts at the top of an existing flexural crack and propagates
into the beam, the crack is referred to as flexural-shear crack (Fig. 5.5). Web-shear cracks occur in
beams with thin webs in regions with high shear and low moment. They are relatively uncommon
cracks and may occur near the inflection points of continuous beams or adjacent to the supports of
simple beams.
Flexural-shear cracks are the most common type found in reinforced concrete beams. A flexural
crack extends vertically into the beam; then the inclined crack forms, starting from the top of
the beam when shear stresses develop in that region. In regions of high shear stresses, beams must
be reinforced by stirrups or by bent bars to produce ductile beams that do not rupture at a failure.
Figure 5.5 Shear failure: (a) general form, (b) web-shear crack, (c) flexural-shear crack,
(d) analysis of forces involved in shear (V a
= interface shear, V z
= shear resistance,
V d
= dowel force).